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#Phase Portraits

Showing: 11 courses
Ross Dynamics Lab

Bifurcation Theory - Saddle-Node, Hopf, Transcritical, Pitchfork

2 rewiews
Explore saddle-node, transcritical, pitchfork, and Hopf bifurcations in dynamical systems. Learn how these phenomena affect phase portraits and system behavior as parameters change.
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7 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Ross Dynamics Lab

Friction and Phase Portraits - Coulomb Friction - Cone of Friction - Falling Broom - Spinning Top

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Explore Coulomb friction, phase portraits, and 3D rigid body dynamics. Analyze friction effects on equilibrium, falling objects, and spinning tops using experiments and mathematical models.
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8 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Ross Dynamics Lab

Phase Portraits from Potential Energy - Bifurcations - Constraint Forces from Lagrange Multipliers

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Explore phase portraits, bifurcations, and constraint forces in dynamical systems. Learn graphical methods, analyze system behavior changes, and understand Lagrangian mechanics with practical applications.
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6 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Ross Dynamics Lab

Lagrange’s Equations with Conservative and Non-Conservative Forces - Phase Space Introduction

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Explore Lagrange's equations for conservative and non-conservative forces, rigid body systems, and phase space analysis. Learn to solve and classify motions using advanced analytical dynamics techniques.
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6 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Steve Brunton

Drawing Phase Portraits for Nonlinear Systems

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Learn to analyze nonlinear systems by drawing phase portraits, identifying fixed points, linearizing, and inferring global dynamics. Gain practical skills in stability analysis using eigenvalues and eigenvectors.
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7 Lesons
26 minutes
On-Demand
Free-Video
Steve Brunton

Systems of ODEs: Imaginary Eigenvalues and Center Fixed Points

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Explore imaginary eigenvalues and center fixed points in 2D ODE systems. Learn to compute eigenvectors, write solutions, and understand geometric intuition behind rotational dynamics.
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7 Lesons
38 minutes
On-Demand
Free-Video
Steve Brunton

Systems of ODEs - Saddle Points and Instability

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Explore unstable saddle points in 2D linear ODEs, their applications in energy-efficient transport, and analysis using eigenvalues, eigenvectors, and phase portraits.
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5 Lesons
28 minutes
On-Demand
Free-Video
Steve Brunton

Examples of Nonlinear Systems - Particle in a Potential Well

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Explore nonlinear systems through the particle in a potential well example, covering Euler-Lagrange equations, vector fields, phase portraits, and damping in engineering mathematics.
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10 Lesons
50 minutes
On-Demand
Free-Video
Steve Brunton

2x2 Systems of ODEs - With Eigenvalues and Eigenvectors, Phase Portraits

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Explore 2x2 systems of ODEs, eigenvalues, eigenvectors, and phase portraits in engineering mathematics. Learn to analyze and visualize complex dynamical systems.
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1 Lesons
49 minutes
On-Demand
Free-Video
Steve Brunton

Linearization of Nonlinear ODEs, 2x2 Systems, Phase Portraits

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Explore linearization techniques for nonlinear ODEs, analyze 2x2 systems, and visualize phase portraits in this advanced engineering mathematics lecture.
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1 Lesons
49 minutes
On-Demand
Free-Video
Artem Kirsanov

Differential Equations: The Language of Change

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Explore dynamical systems and differential equations through intuitive examples. Learn key concepts like state variables, phase portraits, and limit cycles to understand how systems change over time.
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11 Lesons
23 minutes
On-Demand
Free-Video